What does random intercept mean? Is there a difference between random effect and random intercept model?

A random intercept model estimates separate intercepts for each unit of each level at which the intercept is permitted to vary. This is one kind of random effect model. Another kind of random effect model also includes random slopes, and estimates separate slopes (i.e. coefficients, betas, effects, etc. depending on your discipline) for each variable for each unit of each level at which that slope is permitted to vary.

Random effect modelling uses random intercepts to accommodate for multi level structure within data. Random slopes are an extension allowing to describe differences between slopes and correlation between intercepts and slopes.

Why Random Intercepts?

Why not simply include L2 variable in the model as a fixed factor/ control variable?

fine if L2 has few categories

not really interested in difference between counties

if a lot of dummy categories -> eat up a lot of degrees of freedom

Random Intercept + Fixed Slope/ Effects

what?

the slopes for groups are assumed to be of the same value

the structural part of the model is also called fixed effects

why?

The researcher is interested in the characteristics of the sample, not the population

weak effects??

Random Intercept + Random Slope/ Effects

what?

Effects are modelled allowing the slopes to vary between groups.

why?

Enhance computation of fixed effects

Not interested in L2 effects within sample, but in the effects in general population